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24
Problems with the definition of renormalized Hamiltonians for momentumspace renormalization transformations
, 1998
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Gibbsian properties and convergence of the iterates for the BlockAveraging Transformation
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Transformations of Gibbs measures
, 1998
"... We study local transformations of Gibbs measures. We establish sufficient conditions for the quasilocality of the images and obtain results on the existence and continuity properties of their relative energies. General results are illustrated by simple examples. ..."
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We study local transformations of Gibbs measures. We establish sufficient conditions for the quasilocality of the images and obtain results on the existence and continuity properties of their relative energies. General results are illustrated by simple examples.
Almost) Gibbsian description of the sign fields of SOS fields
"... An example is presented of a measure on a lattice system which has a measure zero set of points (configurations) where some conditional probability can be discontinuous, but does not become a Gibbs measure under decimation (or other) transformations. We also discuss some related issues. ..."
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An example is presented of a measure on a lattice system which has a measure zero set of points (configurations) where some conditional probability can be discontinuous, but does not become a Gibbs measure under decimation (or other) transformations. We also discuss some related issues.
Restoration of Gibbsianness for projected and FKG renormalized measures
"... Abstract. We restore part of the thermodynamic formalism for some renormalized measures that are known to be nonGibbsian. We determine a necessary and sufficient condition for consistency with a specification that is quasilocal only in a fixed direction. This condition is then applied to models wi ..."
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Abstract. We restore part of the thermodynamic formalism for some renormalized measures that are known to be nonGibbsian. We determine a necessary and sufficient condition for consistency with a specification that is quasilocal only in a fixed direction. This condition is then applied to models with FKG monotonicity and to models with appropriate "directional continuity rates", in particular to (noisy) decimations or projections of the Ising model. In this way we establish: (i) the validity of the "second part" of the variational principle for projected and FKG blockrenormalized measures, and (ii) the almost quasilocality of FKG blockrenormalized "+" and "−" measures.
Renormalization Group, NonGibbsian states, their relationship and further developments
, 2005
"... We review what we have learned about the “Renormalization Group peculiarities ” which were discovered more than twentyfive years ago by Griffiths and Pearce. We discuss which of the questions they asked have been answered and which ones are still widely open. The problems they raised have led to the ..."
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We review what we have learned about the “Renormalization Group peculiarities ” which were discovered more than twentyfive years ago by Griffiths and Pearce. We discuss which of the questions they asked have been answered and which ones are still widely open. The problems they raised have led to the study of nonGibbsian states (probability measures). We also mention some further related developments, which find applications in nonequilibrium questions and disordered models.
unknown title
, 2003
"... on trees and in mean field Olle H"aggstr"om\Lambda y and Christof K"ulskez ..."
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on trees and in mean field Olle H&quot;aggstr&quot;om\Lambda y and Christof K&quot;ulskez
Université de Rouen, UFR Sciences, site Colbert,
, 2001
"... Variational principle and almost quasilocality ..."
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